'I can't believe I'm so far out of those woods," says Merrill Garbus. For an artist who recorded her first album on a handheld dictaphone in her bedroom, she's come a long way. She spent much the last 10 years broke, sometimes bin-diving to survive, and travelling long hauls between barely paid gigs in her tiny Chevy. But the release of her ramshackle, melody-rich 2009 debut Bird-Brains – released under her performing name of Tune-Yards – which brimmed with ukulele strumming and the sub-Saharan yodelling traditions she studied in Africa, earned Garbus rave reviews and a growing fanbase; not long after its release, she signed with the legendary label 4AD, and can now count Yoko Ono and RZA of the Wu-Tang Clan as fans. The neon face-paint she dons on stage has been scrubbed clean away when we meet in a Manhattan pub; she's wonderfully genial, and her bright pink ski jacket strikes a bold splash of colour against the pub's dark wood panelling.

Tune-Yards began in 2006, after Garbus had moved from New England to Montreal to join her friend Patrick Gregoire in his band, Sister Suvi. Though she'd studied theatre and was an accomplished puppeteer, she'd inherited a love of music from her parents, who were folk musicians. Garbus remembers those early days as an exhilarating time, but also one of worrying about where her next meal would come from. "Patrick was also working on his other band, Islands, so I was there in Montreal – where I was not technically a legal resident – cold and excited, but twiddling my thumbs." Hungry and determined, Garbus picked up her ukulele, found a loop pedal, and launched herself into the DIY community as a one-woman band, playing at friends' houses and basement gigs. "In the beginning, Tune-Yards was this idea that I had so much within me as one person, and that musically, I had so much to say. Once the songs began to unfold themselves, I just had to let them out."

The success of Bird-Brains came as a surprise to Garbus, and she now finds herself trying to recalibrate. "It's completely different to what I know. Money was just never there, so I got used to being and creating without it." The change in fortunes made recording her new LP, Whokill, a period of artistic reassessment. "My first response was to do this album the same way I did the first one, so I started with cheap equipment and a cruddy rehearsal room." The result was a crushing failure. "I mixed the whole album myself and it sounded flat," – she shakes her head at the memory – "I thought I'd failed and that people would hate it; I hated it. The songs just wouldn't wake up, so I asked my friend Eli to help. As someone who likes to do everything themselves, I hate admitting that."

Bird-Brains won hearts for its fuzziness, and for being so obviously the work of one person, so Garbus is anxious about how her fans will react to the evolved sound of Whokill: "There are people who are really dedicated to that from- the-dirt, lo-fi aesthetic, and it may not be to their taste to suddenly hear reverb on my voice." There's a shimmering dub edge to this album, too, particularly on the doo-wop styled lovers' rock harmonies of Doorstep. "Reggae has been a huge influence on me philosophically," Garbus says. "It's in Doorstep, for sure. For such a tiny country, it's incredible how much influence Jamaica has had, all over the world. I'm obsessed with the dub side of things, but there are people who loathe it, so my hope is that Whokill is not so reggae or so dub that they'll hate it."

Along with these Caribbean sounds and "shameless" borrowings from Michael Jackson, Garbus enjoyed tinkering with some of the tools that weren't available to her for Bird-Brains. "With making an album in a studio, I had to confront synths – I had to acknowledge that they exist and that I'd started to really like them," she says, laughing. Another of those tools was another person: Garbus's partner Nate Brenner, who co-wrote a number of tracks and plays bass. Was the lack of low-end strings what led her to create the exuberant percussion that typified Bird-Brains? "Yes!" she laughs. "I had no bass – literally, I didn't own one – so the drums had to be big."

Whokill was originally titled Women Whokill, and was meant to feature an all-female cast of collaborators. With her distinctive face paint and faint brush of upper-lip hair, its no surprise there's a feminist, queer-friendly quality to some of the early figures Garbus found inspiring – Patti Smith, Ani DiFranco and Nina Simone. "I adored Simone when I first came across her, because she didn't fit any typical idea of the feminine voice," Garbus says. "Listening to her, I realised that in music, there is this ability to shake off those stifling ideas about what women are 'meant' to be."

Garbus's own bold, joyfully subversive voice reveals its full range on Whokill, leaping from impassioned tribal growls to soft, hazy lullabies. Dark, confrontational motifs lace her lyrics, the frenetic, zig-zagging saxophones, and wailing, siren-backed choruses seem to build up and release emotional pressure. Garbus found herself using song bridges, a technique she'd previously scoffed at for being "conventional and boring", to convey these shifts. The Beatles rank pretty low on her list of musical inspirations, but she found kindred ground in the Lennon-McCartney model: "McCartney verses were kind of light and happy-go-lucky, but they'd lead up to Lennon's bridges, which were darker and weirder. It's like flipping a coin – it adds another side and depth to the songs."

Garbus also drew on the album's dub aspects to draw out differences. "The dub is sort of the dark side – it's wonderful and horrible simultaneously," she says. This tension is captured in Powa, where the blunted chords of the verses bloom into a cloud of woozy dub harmonies at the bridge. The notes blur into each other, threatening to tip into discord, climaxing with Garbus's yell: "My man likes me from behind/ Tell the truth I never mind/ 'Cos you bomb with life's humiliations every day/ You bomb me so many times I never find my way." "I didn't need to write a song about sex being awesome," she says. "There are plenty of songs like that. And with Powa especially, I was dealing with violence. There's a real middle-class fear of conflict, of the lower classes rising up, of violence in the Middle East. But it's there, it exists; especially violence against women. It's this horrible reality that's always disturbed me, and I wanted to take hold of it in the songs."

Whokill isn't strictly autobiographical – "I allowed myself a lot more fiction and daydreaming in this album" – but the passion of its songs was cast from events in her current home in Oakland, California, specifically the case of Oscar Grant, a young, unarmed African-American man shot and killed by police officer Johannes Mehserle on a subway platform in 2009. The tragedy resulted in a $25m lawsuit against the police department, and riots on the streets. "Doorstep came directly out of the trial of Mehserle," Garbus says. "I saw what was happening in the community and tried to grasp it from some kind of personal perspective. I found the distance between the human experience of that event and the way it was processed by the system horrifying." She remembers a particularly awful moment, standing in front of a graffiti mural pointing out that the NFL player Michael Vick, who had been imprisoned for his part in an illegal dogfighting ring, was given a longer sentence then Mehserle, who was charged with involuntary manslaughter. "How is a person or a community, especially the family who had just lost their son, their loved one, supposed to feel when they see that?"

Is she an activist then, or a musician? "I do feel like I should be doing social justice work sometimes, but I also retain the right to say that this – my music – this is doing enough for the world."